Problem 16 · 2013 Math Kangaroo
Hard
Logic & Word Problems
casework
In the last hockey game there were lots of goals. In the first half 6 goals were scored in total and the visiting team was leading. In the second half the home team scored another three goals and won the match. How many goals did the home team score in total?
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Answer: C — 5
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Hint 1 of 3
In the first half the two teams together scored 6, and the visitors were ahead.
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Hint 2 of 3
List the first-half scores where visitors lead: 6-0, 5-1 or 4-2.
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Hint 3 of 3
Then add the home team's 3 second-half goals and see which case lets them win.
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Approach: test first‑half splits that let home win
- First half the goals add to 6 with visitors ahead, so the splits are visitors 6 home 0, visitors 5 home 1, or visitors 4 home 2.
- The home team then scores 3 more; to win they need their total above the visitors' 6, 5, or 4.
- Only 4-2 works: home ends with \(2 + 3 = 5\) against 4, a win, so the home team scored 5 in total, choice C.
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